Theory of Mobile Communication Matthew Andrews Bell Labs
Theory of Mobile Communication Matthew Andrews Bell Labs Joint with Lisa Zhang February 16, 2006 Background The internet is going mobile Wifi, 3G cellular, picture phones, PDAs, ad-hoc networks Optimization is important Spectrum is limited and expensive No equivalent of putting in another fiber
Need to maximize use of available resources Problems are hard Dynamically changing environments Many interactions between users Overview of talk Some areas of wireless research where TCS ideas are useful A few interesting open problems Some areas of interest
Scheduling Routing Capacity Analysis Congestion Control Addressing Exists a lot of work on wireless problems Vast majority is average case analysis What can TCS provide?
Many tools for worst-case analysis Some areas of interest Scheduling Routing Capacity Analysis Congestion Control Addressing
Is worst case analysis important in wireless networks? No real justification for many statistical assumptions made The most important thing to know about a system is how it breaks P. Fleming, Motorola Wireless scheduling 614.4kbps? 38.4kbps? Choose queue/user Serve distant user at 38.4kbps or close user at 614.4kbps Service rates user dependent!!!! Service rates change over time!!!!
(user mobility, channel fading) Wireless data scheduling model data arrival process DRCi (t) DRCj (t) t service rate vector (DRC1(t),,DRCn (t)) Choose a queue/user to serve at time t If we choose user i, serve at rate DRCi (t) Opportunistic scheduling: Serve user when DRC is high
How do we model the channel? Channel model 1: Stationary stochastic process Service rate vector determined by state of ergodic Markov chain M M(t) (DRC1(t),,DRCn (t)) service rate vector (DRC1(t),,DRCn (t)) Most of the literature works in this model Mobility Mobility destroys stationarity
DRCi (t) How do we model the channel? Channel model 2: Adversarial process Service rate vector determined by adversary Adversary wants scheduler to do bad things service rate vector (DRC1(t),,DRCn (t)) Adversary enables worst-case analysis One interesting question Max Weight (See Tassiulas-Ephremides, Kahale-Wright, Neely-Modiano-Rohrs, Stolyar)
qi(t) = queuesize of user i at time t Serve argmaxi qi(t) * DRCi(t) For stationary channels Potential function i qi(t)2 has negative drift Queues remain stable For adversarial channels ?????? Routing Three types of routing Source Routing Source computes entire route to destination
Useful for traffic engineering, QoS enforcement, Hop-by-hop Routing Send data to neighbor thats advertising good route to dest Good for Shortest Paths Queue-based Routing Each node maintains per-dest queue Send data to neighbor that has short queue protection (disjointness) etc. Routing
Some interesting routing questions What type of routing is most appropriate for dynamic wireless networks How do we do traffic engineering, disjoint paths etc. in dynamic graphs? What is best way to compute shortest paths in wireless networks? How much of dynamic graph literature can be applied? Interested in communication overhead rather than amortized running time Need to be aware of traffic matrix Proactive vs reactive routing Are standard routing algorithms (e.g. AODV, OLSR) optimal? Routing Some interesting routing questions Queue-based routing
Awerbuch-Leighton, Aiello-Kushilevitz-Ostrovsky-Rosen Queue-based routing algorithms are throughput-optimal in static networks What about dynamic wireless networks? Anshelevich-Kempe-Kleinberg, Awerbuch-Berenbrink-Brinkmann-Scheideler Optimality holds for single-sink problem What about general multicommodity case? Congestion Control TCP has well-known problems in wireless networks Packet loss due to interference is perceived as congestion - Fixes:
- Snoop protocol ( Balakrishnan, Seshan, Amir, Katz) - Split connections - Loss prevention: FEC, HARQ, DARQ, link-level retransmissions Buffer sizing is difficult - Buffer size should equal bandwidth-delay product (BDP) - In wireless networks BDP varies due to variable link rate - Leads to excess buffering (>30s buffering in one study) Congestion Control as Network Utility Maximization Wireline networks max Up(xp) subject to
. e p xp ce xp = inj rate on path p ce = capacity of edge e
Kelly-Maulloo-Tan, Low-Lapsley, Low-Peterson-Wang Up(.) = utility function (e.g. log) TCP is a primal dual algorithm for solving above problem Congestion Control as Network Utility Maximization Wireless networks max Up(xp) subject to ( , xp , ) C
C = system capacity region (convex) Depends on power assignments, interference etc. Chiang Joint power control and congestion control for solving problem . xp Congestion Control + Scheduling
Wireless networks max Up(xp) subject to ( , xp , ) C Stolyar, Srikant Joint congestion control and scheduler for solving problem Why is joint congestion control and scheduling important? Need complex scheduler to realize capacity region Dont want scheduler to try and serve empty queue Want large queue to backpressure to source to prevent excess queueing
. . . xp xp Congestion Control + Scheduling Wireless networks max Up(xp) subject to ( , xp , ) C
Question: Previous work on congestion control + scheduling is for stationary wireless channels What about adversarial channels? . . . xp Capacity Analysis Gupta-Kumar
In an n-node ad-hoc networks Throughput per source-dest pair is O(1/n log n) Grossglauser-Tse, El Gamal et al Throughput per source-dest pair is O(1) if nodes move In this work Traffic patterns, node distributions and mobility are uniform How can we evaluate capacity for arbitrary inputs? Capacity Analysis Optimization problem Fixed set of transmitters and receivers Transmission is successful if Signal-to-Noise Ratio is above threshold
Choose powers to maximize aggregate system throughput How hard is this problem? Does it get easier if throughput is weighted by queue length? Addressing In a wireless network: Should my address say who I am or where I am? How do geographic addresses affect routing? locale
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